Technique for inspecting semiconductor wafers

ABSTRACT

A height of a pattern on a semiconductor wafer is determined by comparing a measured image of the pattern with a predicted image of the pattern, as produced by a shadow model. An estimated height of the pattern is provided as an input to the shadow model. The shadow model produces occluding contours that are used to generate predicted images. A set of predicted images are generated, each predicted image being associated with an estimated height. The estimated height corresponding to the predicted image most closely matching with the measured image is used as the height calculated by the shadow model.

RELATED APPLICATION

The present application claims the benefit of priority from U.S.Provisional Application No. 62/508,302, filed May 18, 2017, entitled,“TECHNIQUE FOR INSPECTING SEMICONDUCTOR WAFERS,” which is incorporatedherein by reference in its entirety.

TECHNICAL FIELD

The present disclosure generally relates to inspection of semiconductorwafers, and more specifically, relates to determining height of apattern on a semiconductor wafer using a shadow model.

BACKGROUND

There are some known techniques for measuring dimensions of patternslocated on a semiconductor wafer. It may be needed to measure height (ordepth) of a pattern, or a particular feature of a pattern, such as anoxide recess or a fin of a device. One of the techniques to measureheight is referred to as a “shadow effect.” The technique uses adetector, located at a specific position with respect to the pattern,where the detector does not receive part of the responsive electronsbecause of occlusion by portions of the pattern, such as a sidewall,thereby creating a shadow.

SUMMARY

The following is a simplified summary of the disclosure in order toprovide a basic understanding of some aspects of the disclosure. Thissummary is not an extensive overview of the disclosure. It is intendedto neither identify key or critical elements of the disclosure, nordelineate any scope of the particular implementations of the disclosureor any scope of the claims. Its sole purpose is to present some conceptsof the disclosure in a simplified form as a prelude to the more detaileddescription that is presented later.

In certain implementation, the disclosure performs acomputer-implemented method for determining a height of a pattern on asemiconductor wafer, the method comprising: obtaining a measured imageof the pattern, wherein the measured image of the pattern is indicativeof the height of the pattern; producing, using a shadow model, apredicted image of the pattern, wherein the predicted image isassociated with a function of an estimated height of the pattern, andwherein the estimated height of the pattern is provided as an input tothe shadow model; and, calculating, by a computer processor, the heightof the pattern by comparing the measured image of the pattern with thepredicted image of the shadow of the pattern.

Implementations of the disclosure may also correspond to a system fordetermining a height of a pattern on a semiconductor wafer. The systemincludes a memory; and a computer processor, operatively coupled withthe memory, to perform the following: obtain a measured image of thepattern, wherein the measured image of the pattern is indicative of theheight of the pattern; produce, using a shadow model, a predicted imageof the pattern, wherein the predicted image is associated with afunction of an estimated height of the pattern, and wherein theestimated height of the pattern is provided as an input to the shadowmodel; and, calculate the height of the pattern by comparing themeasured image of the pattern with the predicted image of the shadow ofthe pattern.

In some implementations, a non-transitory computer readable medium mayinclude instructions, which, when executed by a processing device, causethe processing device to perform the above-mentioned tasks.

BRIEF DESCRIPTION OF THE DRAWINGS

The present disclosure will be understood more fully from the detaileddescription given below and from the accompanying drawings of variousimplementations of the disclosure.

FIG. 1 illustrates a system for determining height of a pattern on asemiconductor wafer, in accordance with some embodiments of the presentdisclosure.

FIGS. 2A and 2B show the side view and top view respectively of aschematic set-up of an SEM for scanning a semiconductor wafer with anelectron beam and for detecting distribution of electrons between anumber of electron detectors, in accordance with some embodiments of thepresent disclosure.

FIG. 3A illustrates a functional block diagram schematicallyillustrating the system and its sub-systems, in accordance with someembodiments.

FIG. 3B illustrates a functional block diagram of a particularsub-system, in accordance with some embodiments.

FIG. 4A-4C illustrate shadow computation with an absorption-reflectionmodel, in accordance with some embodiments of the present disclosure.

FIG. 5A illustrates modeling absorption and reflection by a pattern'sedge in order to simulate a shadow as observed from a specific detector,in accordance with some embodiments of the present disclosure.

FIG. 5B shows an SEM image showing a shadow, in accordance with anembodiment of the present disclosure.

FIGS. 6 and 7 schematically illustrate effect of a sidewall for aspecific pixel located near the sidewall, and how it is modeled,according to an embodiment of the present disclosure.

FIG. 8A shows how an occluding contour is generated from a planarcontour of an edge, according to an embodiment of the presentdisclosure.

FIG. 8B shows how a shadow model takes into account area of impact ofeach point on an occluding contour, according to an embodiment of thepresent disclosure.

FIG. 9 is a block diagram of an example computer system in whichimplementations of the present disclosure may operate.

DETAILED DESCRIPTION

Aspects of the present disclosure are directed to inspection of asemiconductor wafer, and specifically, determining height of aparticular pattern on the semiconductor wafer. A “pattern” should beunderstood as one or more features provided on a semiconductor wafer.For the purpose of this disclosure, a pattern typically has a height ordepth that distinguishes it from the wafer's planar base, sometimesreferred to as “valley.” Patterns have sidewalls or edges. A patterncreates a “shadow” due to its height with respect to the valley.

Typically, an electron beam is irradiated on an observation region of asample surface, and an image (for example, a scanning electronmicroscope (SEM) image) is acquired based on a detection signal ofsecondary electrons from a detector disposed obliquely above theobservation region. A length of a shadow of a pattern appearing in theimage is detected. Then, a height of the pattern is calculated by aformula on the basis of the detected length of the shadow and anapparent angle of the detector to the sample surface obtained inadvance. An intensity distribution of the secondary electrons on a lineorthogonal to an edge of the pattern is extracted, and the length of theshadow of the pattern is obtained as a distance between two points wherea recess portion of the intensity distribution intersects apredetermined threshold.

A metrology method known as Critical Dimension SEMs (CD-SEM) may be usedto measure the sidewall angle of a pattern. The height and edge width ofpattern can be measured by the analysis of the signal intensity profileof each channel from multiple detectors in CD-SEM. The edge width ismeasured by the peak width of the signal intensity profile. But it isnot possible to measure the accurate edge width of the pattern, if theedge width is smaller than the primary electron beam diameter.

The above-mentioned CD-SEM approach determines dimensions of features ona semiconductor wafer mainly by utilizing trigonometrical calculationsperformed using precise measurements of the SEMs. None of the techniquesuses a model to calculate the height of a pattern from an estimatedheight rather than requiring a precise on-wafer measurement. The presentdisclosure uses a shadow model to accurately predict a height of apattern without precise on-wafer measurements.

In this disclosure, a height of a pattern on a semiconductor wafer isdetermined by comparing a measured image of the pattern with a predictedimage of the pattern, as produced by a shadow model. An estimated heightof the pattern is provided as an input to the shadow model. The shadowmodel produces occluding contours that are used to generate predictedimages. A set of predicted images are generated, each predicted imagebeing associated with an estimated height. The estimated heightcorresponding to the predicted image most closely matching with themeasured image is used as the height calculated by the shadow model.

Advantages of the present disclosure include, but are not limited to,use of a geometrical algorithm, which is practically not dependent onphysical processes, making the process very robust and reliable.Calibrations needed for the process are the same as that is needed forother wafer inspection techniques, such as height map, i.e. noadditional calibration is needed.

The proposed technique of inspection/measurements can be implementedusing SEM measurements based on all types of electrons, includingsecondary electrons emitted by a surface of a semiconductor wafer inresponse to an electron beam of SEM. Measured images can be obtained bycollecting SEM image data from the detectors and applying signalprocessing to the collected data. Measured image can also be image datapreviously stored.

As has been noted above, the proposed concept enables an alternativeapproach to precise measurements by using shadow images. For example, itallows estimation of the pattern height without performing complexmeasurements but based on measured image data (for example, SEM-images)derived from detecting electrons, since the measured image data may bethen iteratively compared with predicted shadow images modeled by theshadow model, to thereby obtain more accurate estimate of the patternheight.

FIG. 1 illustrates an embodiment comprising a system S3 that has twosub-systems S1 and S3 and a measurement system, such as an SEM. SystemS1 comprises a modeling processor marked as SP1 (which may comprise ahardware unit, software product or software application) associated witha memory (M), for obtaining a predicted image of a pattern on asemiconductor wafer (for example, W) by using a shadow model. The secondsystem S2 further comprises a processor marked SP2 for processing ameasured image, processing the predicted image and comparing it with themeasured image. The systems S1 and S2 may be placed in a free standingcomputer C provided with a display D and a keyboard K. The computer C isin communication with a SEM via a communication line L.

The extended system S3 may further comprise the SEM incorporating asource of an electron beam and one or more detectors which arepositioned so as to monitor the semiconductor wafer W, when inserted inthe SEM, to collect brightness data. SEM may process the collected datainto a measured image or may supply the collected data to the secondsystem S2 for forming and processing the measured image there-inside.

FIGS. 2A and 2B illustrate a set-up for collecting data in the SEM toproduce a measured image. FIG. 2A shows a side view and FIG. 2B showsthe top view. An electron gun G scans the wafer W having a pattern P, byan electron beam of primary electrons PE. Secondary electrons SE, beingproduced by collision of PE with the pattern P on the wafer W, compriseelectrons that are emitted or reflected from the wafer and which aredetected by detectors D0 (top detector), and additional detectors D1,D2, D3, D4, referred to as the split detectors. Each one of thedetectors detects its portion of the SE and thus perceives its specificportion of brightness distribution, depending on location of the patternand on location of the specific detector. FIG. 2A shows an electroncloud EC formed around the location on the wafer (pixel PX) where the PEbeam currently hits pattern P; detectors D0, D1, D2 therefore receivetheir portions of secondary electrons SE created at PX.

FIG. 3A is a block diagram which schematically illustrates sub-system 1(S1) for modeling an predicted image of pattern's shadow onsemiconductor wafer W. Subsystem S1 can be part of another largersubsystem 2 (S2) that uses the model of S1 for determining height of thepattern.

Flowchart 10 in FIG. 3A shows the operation of S1, S2 and S3 incombination with one another. S1 comprises a modeling block 12 whichreceives information on planar contours of the pattern of interest (forexample, from block 14 of S2, or, from a program or an operator), andinformation on the pattern's estimated height. By applying a shadowmodel, block 12 produces a predicted image of shadow for the pattern.The predicted image may be created per detector or as a combinedpredicted image and may further be used for various types of inspectionof the wafer W. It may, for example, be used for determining height ofthe pattern in S2. S2 comprises sub-system S1 that obtains planarcontours from a measured image (block 14). The measured image from theSEM is also fed to the processing block 16 for comparing with predictedimage calculated by modeling block 12. The measured image may be forexample, an image perceived by a specific detector or a combined imagebuilt from per-detector images.

The predicted image is recalculated for various estimated heights, toiteratively arrive at the best height which results in the minimaldifference between the compared pair of real and predicted images. Thepair of images may be compared per pixel, and a cumulative error CE maybe determined for each specific predicted image which was calculated fora specific height value. Upon modeling a set of predicted images for aset of estimated height values, the minimal cumulative error (MCE) maybe determined by system S2, and the best height can be selected as theheight value which brought to the MCE.

System 3 (S3) is an extended system that comprises S2 and SEM (18) withdetectors (not shown) which together supply the measured image data tosystem S2.

FIG. 3B shows simplified method performed by S1 (by modeling block 12).Block 12 receives information on planar (2D) contours of the pattern andon estimated height thereof. First, a shadow model is used to modelabsorption (that results in the actual shadow or low brightness regions)and reflection (that results in the bright regions) around the patternfor one or more specific detectors. The model is thus sometimes calledan absorption-reflection model. The method proceeds to finding areflection coefficient and other parameters characterizing materials ofthe wafer, for further simulation. The method then proceeds to simulatepredicted image(s) for the detector/s based on results of the first andthe second steps. The predicted image(s) may be per detector images or acumulative image.

The model (and the modeling step of the method) may comprise determiningan occluding contour being a line connecting two or more shadowingpoints (or edge points), wherein the shadowing points have an estimatedheight of the pattern and affect propagation of the electrons to thespecific detector. The shadowing points are calculated based on an edgedetection technique. The planar contours of the pattern are transformedby the model into an occluding contour per detector. The model does notdepend on which edge detection technique is used to identify theshadowing points.

The model allows building a multi-pixel brightness picture (being thepredicted image) of the pattern for each of the detectors. The “shadow”model allows predicting a picture of distribution of brightness expectedon and around the pattern, created by the determined planar (2D) contourhaving an estimated value of the pattern height and observed from atleast one specific detector.

In further details, the model is designed to predict, per pixel, thechange in observed brightness (as viewed in each of the detectors),based on at least some of the following considerations: proximity of aspecific pixel to a neighboring occluding contour, the estimated heightcorresponding to neighboring occluding contour, and, relative positionbetween said pixel, said neighboring occluding contour and the detector(since electrons occluded by that contour from one detector may bepartially reflected towards another detector).

The absolute brightness of a pixel also depends on additionalinformation: the material of the surface, the parameters of the electronbeam and the parameters of a detector. When all such additionalinformation is provided, intensity of each pixel can be computed infull. When such additional information is absent, the model allows tocompute relative change in pixel brightness, compared for example toanother pixel located further away from an occluding pattern; theprovided assumption can be made about same material properties for bothpixels, or relative to pixels of some canonical pattern in another imagetaken under similar conditions, where all material and geometricalproperties are known in advance.

In cases when the model is not full, for example when wafer materialinformation is missing, the simulated and the measured images may bebrought to the similar range of grey-level values before the comparison.For example, certain chosen area in both images, such as some placeassumed to be not occluded, can be brought to be of a certain grey levelin both images by way of mathematical operations which are applied toentire images. This will make comparison of images, by way ofsubtracting one from another, meaningful.

FIG. 4A schematically shows the basic function of a shadow model knownas the absorption-reflection model. When SEM beam impinges on a surfaceon the wafer, secondary electrons (SE) are emitted. When SE collideswith the sidewall (edge), a part of them is absorbed (at absorption rater_(a)), and another part of them is reflected (at reflection rater_(r)), such that (r_(a)+r_(r))=1. The assumption is that the reflectionis mirror-like. D1 and D2 are detectors along the SE line-of-sight andon the side, respectively, such that when SE is reflected by thesidewall, D2 detects a signal from reflected electrons, and D1 detectssignal from absorbed electrons. The model assumes that profile patternis trapezoidal (as shown in FIG. 5A), and the sidewalls (edges) arelocally smooth. FIG. 4B shows that in the shadow model, it is assumedthat in the valley, Lambertian distribution L is flat and isotropic inazimuth. FIG. 4C shows that in the shadow model, at the edges(sidewalls), Lambertian is tilted and is not isotropic in azimuth. Thegradient is needed in order to estimate the direction of the Lambertian.

Some of the modeling steps will be explained in more details with theaid of FIGS. 5-7 below.

FIG. 5A and FIG. 5B show what happens on the pattern P upon irradiatinga specific pixel PX of the wafer W with primary electrons PE (FIG. 5A)and how the real SEM image is seen by D1 (left detector, shown also onFIG. 5B). The left hand side of the pattern P is brighter, since aconsiderable portion R_(C) of secondary electrons SE of the electroncloud EC s with the pattern P and then are partially reflected (portionof those reflected electrons is marked R_(R)). At the same time, part ofthe colliding electrons is absorbed (R_(S)). The reflected electrons mayreach detector D1 and may be other detectors (not shown for clarity).

In FIG. 5B, it is shown that the right hand side of the pattern P isdarker (shadowed). Reflection rate R_(R) (say, a fraction ˜0.12, i.e.12% of the colliding electrons R_(C)) and absorption rate R_(S)(s-shadow) may be modeled as being proportional to collision rate R_(C).

In presence of a neighboring pattern/feature P, electrons yielding fromthe wafer can be absorbed by a feature edge and create shadow, asindicated by the absorption fraction (R_(S)), or, change its directionand reach one or another detector thus creating reflection, as indicatedby the reflection fraction (R_(R)). Rates R_(S) and R_(R) areproportional to collision rate R_(C). The relationship is simplifiedinto the equation, R_(S)=R_(C)−R_(R). In other words, the shadow modelis indicative of loss of yield caused by shadowing, where the loss ofyield is caused by the absorption of electrons by the sidewall of thepattern, or by reflection of light away from the detector, where theterm “yield” refers to the signal at the detector.

FIG. 6 schematically illustrates how the collision rate R_(C) may bedetermined. The illustration shows a pattern P and a pixel of interestPX on the valley part of wafer W, where ϕ is an elevation angle betweenthe pixel and the pattern P's sidewall, and Θ is an azimuthal angle onthe wafer W (where dΘ is the angular distance between two points). Thecalculations allow determining a portion of colliding electrons for thespecific angle Θ, followed by the calculation for all angles Θ, therebyenabling to estimate the shadow resulting from the colliding electronsas would be detected by the detector D1.

The azimuthal differential of the electrons hitting the side wall can beexpressed by the equation:

O_(i)(θ) = p(e ∈ φ₁, e ∈ Side, θ) = ∫₀^(φ₁(θ))F_(S)(φ)L(φ, θ, φ₀, θ₀)d φ

wherein, i=number of a detector, L=Lambertian distribution, ϕ=angularheight of the neighbor pattern, F_(i)(ϕ, θ)=probability of reachingdetector for a SE with direction (ϕ, θ), (ϕ₀, θ₀)=elevation and azimuthof normal vector of local surface.

Total collision rate is

$R_{c}\overset{def}{=}{{P\left( {{e \in \varphi_{1}},{e \in {Side}}} \right)} = {\int_{0}^{2\pi}{{O_{i}(\theta)}d\; \theta}}}$

As described above, collision is divided between absorption andreflection. Reflection is computed by subtracting a part of the electronrate of the “target” detector and adding this part to another “mirror”detector (as mentioned with reference to FIG. 4A)

FIG. 7 schematically illustrates and explains how the predicted shadowimage may be modeled in a valley region between pattern edges. Surfacenormal is a plain valley surface of W. Angular shadowing in sidedetectors is an expression determining probability of a secondaryelectron to collide with the wall of P within the angle ϕ, as a functionof angle θ (see FIG. 6). Shadowing in side detectors in a sector θallows determining probability of colliding (and thus shadowing withinθ) for a specific detector, say D1. For example, shadowing can beexpressed as follows for the angle ϕ1, height Δh and distance Δr fromthe pattern P edge:

${{{Surface}\mspace{14mu} {normal}} = \left( {\frac{\pi}{2},0} \right)};{\tau = {{{tg}\; \varphi_{1}} = \frac{\Delta \; h}{\Delta \; r}}}$${O(\tau)}\overset{def}{=}{\int_{0}^{{arctg}{(\tau)}}{{F_{S}(\varphi)}{L\left( {\varphi,0,\frac{\pi}{2},0} \right)}d\; \varphi}}$${{{Surface}\mspace{14mu} {normal}} = \left( {\frac{\pi}{2},0} \right)};{\tau = {{{tg}\; \varphi_{1}} = \frac{\Delta \; h}{\Delta \; r}}}$

Angular shadowing in side detectors can be expressed as:

${O_{a}(\theta)}\overset{def}{=}{{p\left( {{e \in \varphi_{1}},{e \in {Side}},\theta} \right)} = {O\left( {\tau (\theta)} \right)}}$

Shadowing in side detectors in a sector Θ can be expressed as:

$R_{c}\overset{def}{=}{{P\left( {{e \in \varphi_{1}},{e \in {Side}}} \right)} = {\int_{\Theta}^{\;}{{O_{a}(\theta)}d\; \theta}}}$

The absorption and the reflection may be finally processed as follows,for determining shadow of a pattern for a specific detector. Detectorsignal Ri is formed based on a signal rate (portion) on the open areaRio and depends on the portion of absorbed electrons (R_(S)) and aportion which was reflected to that detector from another direction(R_(R)): R_(i)=R_(io)*(1−R_(S)+R_(R)).

The formula of the shadow model, which allows describing the shadowdetected by a specific detector, may be written down as follows:

$R_{i} = {R_{i\; 0} - R_{ci} + {\sum\limits_{k \neq i}{R_{ck} \cdot \rho_{R}}}}$

wherein R_(Ci) is a rate (portion) of electrons which were directed toour specific i^(th) detector but not arrived to it due to collision;R_(Ck) is a rate (portion) of electrons which were directed to another,kth detector (k≠i) but due to collision could arrive to our i^(th)detector; ρR is a reflection coefficient estimating which part of thecolliding electrons was reflected.

The above formula of the shadow model indicates that the signal R_(i)which could be received by a specific i^(th) detector owing to electronswhich would arrive to that detector from a semiconductor wafer scannedby an electron beam, depends on proportion of the electrons which a)would arrive to the detector directly and b) would collide with aspecific pattern on the wafer and arrive to the i^(th) detectorpartially and/or indirectly. To determine the signal, the shadow modeltakes into consideration geometric position of a specific pixel on thewafer relative to neighboring patterns, height of the neighboringpatterns, absorption of electrons by the neighboring patterns andreflection of electrons from the neighboring patterns.

FIG. 8A shows an example of an occluding contour generated by a shadowmodel from the planar contour of an edge of a pattern, e.g., the patternshown in FIG. 5B. The X and Y axes are arbitrary dimensions (not toscale). The occluding contour is generated only from the parts of theedge that actually produce the shadow. Other points in the planarcontour are not important for the absorption-reflection model.

FIG. 8B shows how the occluding contour is generated from a 2D planarcontour. For example, point A is an edge point on the planar contourthat impacts the areas covered by line segments L1 and L2. Segments L1and L2 are part of the occluding contour. Point B impacts the areacovered by the dashed line segment L3 (between points C and D). Ingeneral, the shadow model estimates impacted points for each point ofoccluding contour for each direction, and add shadow values to theimpacted points.

The shadow model produces a predicted image from the occluding contour.A set of predicted images are generated, each predicted image beingassociated with an estimated height. Each predicted image is comparedwith the measured image. The comparison is made under the assumptionthat the height of the pattern in the measured field of view issubstantially the same. If that is not the case, the field of view canbe changed. This can be done during the set-up stage during measurement,and not part of the modeling process. With proper field of vie set, theestimated height corresponding to the predicted image that is theclosest match with the measured image (e.g. image obtained from the SEM)is determined to be the height of the pattern.

FIG. 9 illustrates an example machine of a computer system 900 withinwhich a set of instructions, for causing the machine to perform any oneor more of the methodologies discussed herein, may be executed. Inalternative implementations, the machine may be connected (e.g.,networked) to other machines in a LAN, an intranet, an extranet, and/orthe Internet. The machine may operate in the capacity of a server or aclient machine in client-server network environment, as a peer machinein a peer-to-peer (or distributed) network environment, or as a serveror a client machine in a cloud computing infrastructure or environment.

The machine may be a personal computer (PC), a tablet PC, a set-top box(STB), a Personal Digital Assistant (PDA), a cellular telephone, a webappliance, a server, a network router, a switch or bridge, or anymachine capable of executing a set of instructions (sequential orotherwise) that specify actions to be taken by that machine. Further,while a single machine is illustrated, the term “machine” shall also betaken to include any collection of machines that individually or jointlyexecute a set (or multiple sets) of instructions to perform any one ormore of the methodologies discussed herein.

The example computer system 900 includes a processing device 902, a mainmemory 904 (e.g., read-only memory (ROM), flash memory, dynamic randomaccess memory (DRAM) such as synchronous DRAM (SDRAM) etc.), a staticmemory 909 (e.g., flash memory, static random access memory (SRAM),etc.), and a data storage device 916, which communicate with each othervia a bus 908.

Processing device 902 represents one or more general-purpose processingdevices such as a microprocessor, a central processing unit, or thelike. More particularly, the processing device may be complexinstruction set computing (CISC) microprocessor, reduced instruction setcomputing (RISC) microprocessor, very long instruction word (VLIW)microprocessor, or processor implementing other instruction sets, orprocessors implementing a combination of instruction sets. Processingdevice 902 may also be one or more special-purpose processing devicessuch as an application specific integrated circuit (ASIC), a fieldprogrammable gate array (FPGA), a digital signal processor (DSP),network processor, or the like. The processing device 902 is configuredto execute instructions for performing the operations and stepsdiscussed herein.

The computer system 900 may further include a network interface device922 to communicate over the network 918. The computer system 900 alsomay include a video display unit 910 (e.g., a liquid crystal display(LCD) or a cathode ray tube (CRT)), an alphanumeric input device 912(e.g., a keyboard), a cursor control device 914 (e.g., a mouse), agraphics processing unit, a signal generation device (e.g., a speaker)920, graphics processing unit, video processing unit, and audioprocessing unit. Some of the units are not specifically shown.

The data storage device 916 may include a machine-readable storagemedium 924 (also known as a computer-readable medium) on which is storedone or more sets of instructions or software embodying any one or moreof the methodologies or functions described herein. The instructions mayalso reside, completely or at least partially, within the main memory904 and/or within the processing device 902 during execution thereof bythe computer system 900, the main memory 904 and the processing device902 also constituting machine-readable storage media.

In one implementation, the instructions include instructions toimplement functionality corresponding to the method of determiningheight, as disclosed herein. While the machine-readable storage medium924 is shown in an example implementation to be a single medium, theterm “machine-readable storage medium” should be taken to include asingle medium or multiple media (e.g., a centralized or distributeddatabase, and/or associated caches and servers) that store the one ormore sets of instructions. The term “machine-readable storage medium”shall also be taken to include any medium that is capable of storing orencoding a set of instructions for execution by the machine and thatcause the machine to perform any one or more of the methodologies of thepresent disclosure. The term “machine-readable storage medium” shallaccordingly be taken to include, but not be limited to, solid-statememories, optical media and magnetic media.

Some portions of the preceding detailed descriptions have been presentedin terms of algorithms and symbolic representations of operations ondata bits within a computer memory. These algorithmic descriptions andrepresentations are the ways used by those skilled in the dataprocessing arts to most effectively convey the substance of their workto others skilled in the art. An algorithm is here, and generally,conceived to be a self-consistent sequence of operations leading to adesired result. The operations are those requiring physicalmanipulations of physical quantities. Usually, though not necessarily,these quantities take the form of electrical or magnetic signals capableof being stored, combined, compared, and otherwise manipulated. It hasproven convenient at times, principally for reasons of common usage, torefer to these signals as bits, values, elements, symbols, characters,terms, numbers, or the like.

It should be borne in mind, however, that all of these and similar termsare to be associated with the appropriate physical quantities and aremerely convenient labels applied to these quantities. Unlessspecifically stated otherwise as apparent from the above discussion, itis appreciated that throughout the description, discussions utilizingterms such as “identifying” or “determining” or “calculating,”“executing” or “performing” or “collecting” or “creating” or “sending”or the like, refer to the action and processes of a computer system, orsimilar electronic computing device, that manipulates and transformsdata represented as physical (electronic) quantities within the computersystem's registers and memories into other data similarly represented asphysical quantities within the computer system memories or registers orother such information storage devices.

The present disclosure also relates to an apparatus for performing theoperations herein. This apparatus may be specially constructed for theintended purposes, or it may comprise a general purpose computerselectively activated or reconfigured by a computer program stored inthe computer. Such a computer program may be stored in a computerreadable storage medium, such as, but not limited to, any type of diskincluding floppy disks, optical disks, CD-ROMs, and magnetic-opticaldisks, read-only memories (ROMs), random access memories (RAMs), EPROMs,EEPROMs, magnetic or optical cards, or any type of media suitable forstoring electronic instructions, each coupled to a computer system bus.

The algorithms and displays presented herein are not inherently relatedto any particular computer or other apparatus. Various general purposesystems may be used with programs in accordance with the teachingsherein, or it may prove convenient to construct a more specializedapparatus to perform the method. The structure for a variety of thesesystems will appear as set forth in the description below. In addition,the present disclosure is not described with reference to any particularprogramming language. It will be appreciated that a variety ofprogramming languages may be used to implement the teachings of thedisclosure as described herein.

The present disclosure may be provided as a computer program product, orsoftware, that may include a machine-readable medium having storedthereon instructions, which may be used to program a computer system (orother electronic devices) to perform a process according to the presentdisclosure. A machine-readable medium includes any mechanism for storinginformation in a form readable by a machine (e.g., a computer). Forexample, a machine-readable (e.g., computer-readable) medium includes amachine (e.g., a computer) readable storage medium such as a read onlymemory (“ROM”), random access memory (“RAM”), magnetic disk storagemedia, optical storage media, flash memory devices, etc.

In the foregoing specification, implementations of the disclosure havebeen described with reference to specific example implementationsthereof. It will be evident that various modifications may be madethereto without departing from the broader spirit and scope ofimplementations of the disclosure as set forth in the following claims.The specification and drawings are, accordingly, to be regarded in anillustrative sense rather than a restrictive sense.

What is claimed is:
 1. A computer-implemented method for determining aheight of a pattern on a semiconductor wafer, the method comprising:obtaining a measured image of the pattern, wherein the measured image ofthe pattern is indicative of the height of the pattern; producing, usinga shadow model, a predicted image of the pattern, wherein the predictedimage is associated with a function of an estimated height of thepattern, and wherein the estimated height of the pattern is provided asan input to the shadow model; and calculating, by a computer processor,the height of the pattern by comparing the measured image of the patternwith the predicted image of the shadow of the pattern.
 2. The method ofclaim 1, wherein obtaining the measured image comprises using collectingimage data from one or more side detectors.
 3. The method of claim 1,wherein producing the predicted image further comprises: producing anoccluding contour from planar contours of pattern edges that aredetermined to be occluding edges.
 4. The method of claim 3, wherein themethod further comprises: for each point of an occluding contour, foreach direction, estimating what other points are impacted, and, adding ashadow value to each of the impacted points.
 5. The method of claim 4,wherein an edge detection technique is used to identify edge points. 6.The method of claim 4, wherein the method further comprises: using theoccluding contour to generate the predicted image to be compared withthe measured image.
 7. The method of claim 6, wherein the method furthercomprises: generating a set of predicted images, each predicted imagebeing associated with a respective estimated height.
 8. The method ofclaim 7, wherein the method further comprises: comparing the measuredimage with each of the predicted images; selecting the predicted imagethat matches most closely with the measured image; and using theestimated height associated with the selected predicted image to be thecalculated height of the pattern.
 9. The method of claim 1, wherein theshadow model is indicative of loss of yield caused by shadowing.
 10. Asystem for determining a height of a pattern on a semiconductor wafer,the system comprising: a memory; and a computer processor, operativelycoupled with the memory, to: obtain a measured image of the pattern,wherein the measured image of the pattern is indicative of the height ofthe pattern; produce, using a shadow model, a predicted image of thepattern, wherein the predicted image is associated with a function of anestimated height of the pattern, and wherein the estimated height of thepattern is provided as an input to the shadow model; and calculate theheight of the pattern by comparing the measured image of the patternwith the predicted image of the shadow of the pattern.
 11. The system ofclaim 10, wherein the measured image of the pattern is produced bycollecting image data from one or more side detectors.
 12. The system ofclaim 10, wherein the system produces an occluding contour from planarcontours of pattern edges that are determined to be occluding edges. 13.The system of claim 12, wherein, for each point of an occluding contour,for each direction, the system estimates what other points are impacted,and, adds a shadow value to each of the impacted points.
 14. The systemof claim 13, wherein an edge detection technique is used to identifyedge points.
 15. The method of claim 13, wherein the occluding contouris used to generate the predicted image to be compared with the measuredimage.
 16. The method of claim 15, wherein a set of predicted images isgenerated, each predicted image being associated with a respectiveestimated height.
 17. The system of claim 16, wherein the system furtherperforms: comparing the measured image with each of the predictedimages; selecting the predicted image that matches most closely with themeasured image; and using the estimated height associated with theselected predicted image to be the calculated height of the pattern. 18.The system of claim 10, wherein the shadow model is indicative of lossof yield caused by shadowing.